Objection 1. It would seem that our intellect can know immaterial substances through the knowledge of material things. For Dionysius says (Coel. Hier. i) that "the human mind cannot be raised up to immaterial contemplation of the heavenly hierarchies, unless it is led thereto by material guidance according to its own nature." Therefore we can be led by material things to know immaterial substances.
Objection 2. Further, science resides in the intellect. But there are sciences and definitions of immaterial substances; for Damascene defines an angel (De Fide Orth. ii, 3); and we find angels treated of both in theology and philosophy. Therefore immaterial substances can be understood by us.
Objection 3. Further, the human soul belongs to the genus of immaterial substances. But it can be understood by us through its act by which it understands material things. Therefore also other material substances can be understood by us, through their material effects.
Objection 4. Further, the only cause which cannot be comprehended through its effects is that which is infinitely distant from them, and this belongs to God alone. Therefore other created immaterial substances can be understood by us through material things.
On the contrary, Dionysius says (Div. Nom. i) that "intelligible things cannot be understood through sensible things, nor composite things through simple, nor incorporeal through corporeal."
I answer that, Averroes says (De Anima iii) that a philosopher named Avempace [Ibn-Badja, Arabian Philosopher; ob. 1183 taught that by the understanding of natural substances we can be led, according to true philosophical principles, to the knowledge of immaterial substances. For since the nature of our intellect is to abstract the quiddity of material things from matter, anything material residing in that abstracted quiddity can again be made subject to abstraction; and as the process of abstraction cannot go on forever, it must arrive at length at some immaterial quiddity, absolutely without matter; and this would be the understanding of immaterial substance.
Now this opinion would be true, were immaterial substances the forms and species of these material things; as the Platonists supposed. But supposing, on the contrary, that immaterial substances differ altogether from the quiddity of material things, it follows that however much our intellect abstract the quiddity of material things from matter, it could never arrive at anything akin to immaterial substance. Therefore we are not able perfectly to understand immaterial substances through material substances.
Reply to Objection 1. From material things we can rise to some kind of knowledge of immaterial things, but not to the perfect knowledge thereof; for there is no proper and adequate proportion between material and immaterial things, and the likenesses drawn from material things for the understanding of immaterial things are very dissimilar therefrom, as Dionysius says (Coel. Hier. ii).
Reply to Objection 2. Science treats of higher things principally by way of negation. Thus Aristotle (De Coel. i, 3) explains the heavenly bodies by denying to them inferior corporeal properties. Hence it follows that much less can immaterial substances be known by us in such a way as to make us know their quiddity; but we may have a scientific knowledge of them by way of negation and by their relation to material things.
Reply to Objection 3. The human soul understands itself through its own act of understanding, which is proper to it, showing perfectly its power and nature. But the power and nature of immaterial substances cannot be perfectly known through such act, nor through any other material thing, because there is no proportion between the latter and the power of the former.
Reply to Objection 4. Created immaterial substances are not in the same natural genus as material substances, for they do not agree in power or in matter; but they belong to the same logical genus, because even immaterial substances are in the predicament of substance, as their essence is distinct from their existence. But God has no connection with material things, as regards either natural genus or logical genus; because God is in no genus, as stated above (Question 3, Article 5). Hence through the likeness derived from material things we can know something positive concerning the angels, according to some common notion, though not according to the specific nature; whereas we cannot acquire any such knowledge at all about God.
Source: Summa Theologica (New Advent)